11.3 Sensitivity analysis and risk assessment
2 min read•july 24, 2024
Sensitivity analysis techniques help decision-makers understand how changes in variables affect outcomes. From one-way analysis to Monte Carlo simulations, these methods reveal which factors matter most. Tornado diagrams visually rank variables by impact, guiding where to focus efforts.
Risk assessment tools aid in evaluating decision alternatives under uncertainty. quantifies the worth of reducing uncertainty. Various risk measurement techniques and decision criteria help managers navigate complex choices while considering their risk preferences.
Sensitivity Analysis Techniques
Sensitivity analysis for decision impact
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Top images from around the web for Sensitivity analysis for decision impact
Estimating Value at Risk using Python: Measures of exposure to financial risk View original
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SE - Topological analysis in Monte Carlo simulation for uncertainty propagation View original
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- varies one variable at a time observing changes in optimal decision (interest rates)
- varies two variables simultaneously creating 2D graph visualizing decision regions (price vs demand)
- identifies point where optimal decision changes (break-even point)
- evaluates best-case, worst-case, and most likely scenarios (economic boom, recession, steady growth)
- generates random values for uncertain variables running multiple iterations to assess overall impact (stock market fluctuations)
Critical variables in tornado diagrams
- construction lists variables on vertical axis showing impact range on horizontal axis
- Variable ranking orders variables from most to least impactful
- Interpretation of tornado diagrams wider bars indicate higher sensitivity narrower bars suggest lower sensitivity
- Steps to create a tornado diagram:
- Identify key variables
- Determine reasonable range for each variable
- Calculate outcome for each variable's high and low values
- Sort variables by impact magnitude
- Applications in decision-making focus on high-impact variables for further analysis allocate resources to reduce uncertainty in critical variables (market demand, production costs)
Risk Assessment and Decision-Making
Expected value of perfect information
- maximum amount decision-maker would pay for perfect information
- Calculation of EVPI where is expected value with perfect information and is expected value of best alternative without perfect information
- for EVPI constructs decision trees with and without perfect information comparing expected values
- Applications of EVPI determine value of additional research or data collection assess whether to invest in reducing uncertainty (market research, geological surveys)
- Limitations of EVPI assumes decision-maker may overestimate value of information in practice
Risk assessment in decision alternatives
- Risk measurement techniques include of outcomes of outcomes
- Probability distributions for risk assessment
- Risk attitudes risk-neutral
- uses utility functions to represent risk preferences for decision-making
- Risk-adjusted decision criteria (RANPV)
- Portfolio theory concepts to reduce risk
- Decision-making under uncertainty:
- (pessimistic approach)
- (optimistic approach)
- (weighted approach)
Key Terms to Review (28)
Certainty Equivalent: The certainty equivalent is the guaranteed amount of money that an individual would consider equally desirable as a risky prospect with a higher expected value. This concept highlights how people perceive and react to risk, as it demonstrates their risk aversion or risk tolerance by revealing the trade-off between guaranteed outcomes and uncertain gains.
Coefficient of variation: The coefficient of variation (CV) is a statistical measure that represents the ratio of the standard deviation to the mean, expressed as a percentage. It provides a way to assess the relative variability of data sets, allowing for comparisons between different distributions or data sets that may have different units or scales. A higher CV indicates greater variability relative to the mean, while a lower CV suggests less variability.
Decision tree analysis: Decision tree analysis is a visual and analytical decision-making tool that helps in making informed choices by representing various alternatives, possible outcomes, and their associated risks. It enables decision-makers to evaluate the implications of each choice in a structured way, facilitating understanding of complex decisions and allowing for better risk assessment. This method highlights the importance of sensitivity analysis, as it helps in identifying how changes in variables affect potential outcomes, and raises ethical considerations related to the data used in forming the decisions.
Diversification: Diversification is the strategy of spreading investments across various assets, industries, or markets to reduce overall risk. By investing in a diverse range of assets, individuals and organizations can minimize the impact of any single asset's poor performance on their overall portfolio, thus enhancing stability and potential returns. This approach is particularly relevant in understanding how changes in market conditions can affect different investments, highlighting the importance of balancing risk and return.
Efficient frontier: The efficient frontier is a concept in modern portfolio theory that represents a set of optimal investment portfolios that offer the highest expected return for a given level of risk. It showcases the trade-off between risk and return, helping investors make informed decisions by identifying portfolios that maximize returns while minimizing risk exposure. Understanding the efficient frontier is crucial for effective risk assessment and sensitivity analysis, as it allows for evaluating how changes in investment choices impact overall portfolio performance.
EVPI: Expected Value of Perfect Information (EVPI) is a decision-making tool that quantifies the value of having complete and perfect information before making a choice. It represents the maximum amount a decision-maker should be willing to pay for information that eliminates uncertainty regarding future events, helping in assessing the trade-off between the cost of obtaining information and the potential benefits it brings to decision-making.
Expected Utility: Expected utility is a concept in decision theory that quantifies the overall satisfaction or value a decision-maker anticipates from different outcomes, weighted by the probabilities of those outcomes occurring. This approach helps individuals or organizations make choices under uncertainty by comparing the expected utilities of various options, allowing for more rational decision-making processes. By integrating both the desirability of outcomes and their likelihood, expected utility becomes a critical component in understanding risk assessment and Bayesian decision-making.
Expected Value of Perfect Information: The expected value of perfect information (EVPI) is the maximum amount a decision-maker would be willing to pay for information that would eliminate uncertainty about the outcomes of a decision. It quantifies the value of having complete and accurate information before making a decision, highlighting how better information can improve decision-making by reducing risk and leading to better outcomes.
Hurwicz Criterion: The Hurwicz criterion is a decision-making approach used under uncertainty that combines optimism and pessimism by weighing the best and worst possible outcomes. This method helps decision-makers evaluate options by assigning a coefficient of optimism to the best outcome and a coefficient of pessimism to the worst outcome, allowing for a balance between risk and reward in uncertain situations.
Maximax criterion: The maximax criterion is a decision-making approach that focuses on maximizing the maximum possible payoff. It is primarily used in situations where decision-makers are optimistic and are willing to take risks to achieve the highest potential rewards. This criterion emphasizes a forward-thinking perspective, encouraging individuals to choose the alternative that offers the best possible outcome among all options, regardless of the likelihood of those outcomes occurring.
Maximin Criterion: The maximin criterion is a decision-making approach used under conditions of uncertainty, where the objective is to maximize the minimum possible payoff or outcome. This strategy prioritizes securing the best worst-case scenario, making it particularly useful for managers who aim to minimize risk and protect against potential losses in uncertain environments.
Minimax regret criterion: The minimax regret criterion is a decision-making approach that aims to minimize the maximum possible regret a decision-maker might feel after making a choice. It does this by evaluating the potential regret of each decision based on the best outcome that could have been achieved had different choices been made, allowing for a systematic evaluation of options under uncertainty. This approach connects with concepts such as risk assessment, where understanding potential outcomes is crucial, and sensitivity analysis, which examines how changes in assumptions can impact decisions.
Monte Carlo simulation: Monte Carlo simulation is a statistical technique that uses random sampling and repeated simulations to model and analyze complex systems or processes, particularly under conditions of uncertainty. This method helps decision-makers understand the impact of risk and uncertainty by generating a range of possible outcomes, enabling informed decision-making.
Normal Distribution: Normal distribution is a continuous probability distribution that is symmetric about the mean, depicting that data near the mean are more frequent in occurrence than data far from the mean. This characteristic makes it a cornerstone in statistics, as many natural phenomena and measurement errors follow this pattern, connecting it to concepts such as estimation, sampling distributions, and risk assessment in management.
One-way sensitivity analysis: One-way sensitivity analysis is a technique used to assess how changes in a single variable can impact the outcome of a decision model. This method isolates one variable at a time while keeping all others constant, allowing decision-makers to understand the degree of sensitivity in their model's results. By focusing on one variable, it simplifies the analysis and highlights the importance of each input in driving overall outcomes, making it essential for risk assessment and decision-making.
Risk-adjusted net present value: Risk-adjusted net present value (rNPV) is a financial metric that accounts for the uncertainty and risk associated with future cash flows of an investment by adjusting the discount rate used to calculate the net present value (NPV). By incorporating risk factors into the discount rate, rNPV provides a more accurate representation of an investment's potential profitability, allowing decision-makers to assess the viability of projects under various scenarios.
Risk-averse: Risk-averse refers to a person's or organization's preference for certainty over uncertainty when making decisions, especially in financial contexts. This behavior reflects a desire to avoid potential losses rather than to seek out potential gains, often leading to conservative choices. Risk-averse individuals or entities may prioritize stability and security over higher but uncertain returns.
Risk-neutral: Risk-neutral refers to an attitude toward risk where an individual or entity is indifferent to the potential outcomes of a decision, valuing them solely based on their expected value. This perspective implies that the decision-maker does not have a preference for either risk or certainty and will focus primarily on maximizing expected returns rather than minimizing risk exposure. In the context of assessing decisions, being risk-neutral can significantly influence the evaluation of alternatives and the outcomes of sensitivity analyses.
Risk-seeking: Risk-seeking refers to a decision-making behavior where individuals or organizations prefer options with higher risk and potentially higher rewards over safer alternatives. This tendency often drives people to make choices that involve uncertainty, motivated by the possibility of achieving significant gains despite the dangers involved. Understanding risk-seeking behavior is crucial in sensitivity analysis and risk assessment, as it can significantly affect the outcomes and strategies employed in decision-making processes.
Scenario analysis: Scenario analysis is a strategic planning tool used to evaluate the potential outcomes of various future events by considering different possible scenarios. It helps organizations assess how uncertainties might impact their decisions and operations, enabling them to make more informed choices. This method is closely linked with other analytical techniques, as it can enhance decision-making processes by providing a clearer picture of risks and opportunities in various contexts.
Standard Deviation: Standard deviation is a measure of the amount of variation or dispersion in a set of values, indicating how much the individual data points differ from the mean. It helps in understanding the spread of data and is critical for assessing reliability and consistency in various analyses.
Threshold analysis: Threshold analysis is a decision-making tool used to determine the point at which a change in a variable significantly impacts the outcome of a model or system. This approach helps identify critical thresholds that, once crossed, may result in substantial shifts in risk or sensitivity, providing insights into how different factors influence overall results.
Tornado diagram: A tornado diagram is a graphical representation used in sensitivity analysis to display the relative importance of different variables on an outcome. It helps visualize how changes in inputs can affect the outputs, making it easier to identify which factors have the most significant impact on a particular decision or forecast.
Triangular distribution: The triangular distribution is a continuous probability distribution characterized by a lower limit, an upper limit, and a peak or most likely value. This distribution is particularly useful in risk assessment and sensitivity analysis, as it allows for the modeling of uncertain variables with a simple structure that can capture both the variability and the expected outcomes of scenarios.
Two-way sensitivity analysis: Two-way sensitivity analysis is a technique used to assess how changes in two different input variables impact the outcome of a model or decision-making process. This method helps decision-makers understand the relationship between multiple uncertainties and their effects on results, providing insights into potential risks and areas of focus for further investigation.
Uniform distribution: Uniform distribution is a type of probability distribution where all outcomes are equally likely within a specified range. This means that any value within the defined interval has the same probability of occurring, making it a simple yet powerful model for representing random variables. It serves as a foundational concept in various statistical methods, particularly when analyzing continuous data, assessing risks, or performing simulations.
Utility Theory: Utility theory is a framework used in economics and decision-making that quantifies the satisfaction or value an individual derives from a particular outcome or choice. This theory helps in understanding how people make decisions under uncertainty and risk by analyzing preferences and trade-offs between different options. It plays a crucial role in assessing the desirability of various outcomes and supports various analytical methods for improving decision-making processes.
Variance: Variance is a statistical measure that quantifies the degree of dispersion or spread in a set of data points relative to their mean. It helps to understand how much individual data points deviate from the average value, which is crucial for making informed decisions in various fields, including management.